Hope is fading for a California couple who vanished at sea this week off the coast of Mexico.

The U.S. Coastguard halted its search late Saturday for Josh Hartman, 28, and his fiancee, 30-year-old Ana Martin of Oceanside, Calif. after their boat washed up on a beach near Rosarito, Mexico, on Friday, authorities confirmed to FOX News.

Authorities said it is unlikely the couple could survive the 63 degree water temperature.

The 32-foot fishing boat, named "The Pelican," landed ashore just north of Rosarito, a beach community 20 miles south of the border, U.S. Coast Guard Lt. Jeremy Denning said.

Investigators have found no trace of either Hartman, who is an experienced boater, or Martin.

The Coast Guard suspended the 45-hour search for Hartman and Martin after authorities confirmed the boat belonged to the couple.

The Mexican Navy is now presiding over the search for the couple, and reportedly towed the boat back to the U.S. for further investigation.

Authorities told FOX News that several items—-including a life raft, life jackets, and weapons—were found onboard the boat when it washed ashore.

Hartman and Martin were last seen leaving Oceanside Harbor to fish for bait at 7:30 a.m. Thursday, according to Hartman’s mother.

Hartman called his brother that afternoon to say he caught a lot of fish and was heading back, but no one heard from him since, she said.

She said her son was an expert boater who had been working in commercial fishing for more than two years.

"We're praying all the time they're going to come home, and we'll continue to until we find out something else," she told the North County Times.

Hartman and Martin had planned to wed in August.

Click here for more coverage from FOX affiliate XETV in San Diego.

FOX News Casey Stegall in Oceanside, Calif. and the Associate Press contributed to this report.